To solve the inequality \( x + 2 \frac{1}{2} < 8 \), first convert the mixed number into an improper fraction or a decimal.
In decimal form, \( 2 \frac{1}{2} \) is equal to \( 2.5 \).
Now, rewrite the inequality:
\[ x + 2.5 < 8 \]
Next, subtract \( 2.5 \) from both sides to isolate \( x \):
\[ x < 8 - 2.5 \]
Calculating the right side gives:
\[ 8 - 2.5 = 5.5 \]
Thus, the inequality is:
\[ x < 5.5 \]
Rearranging it to have \( x \) first, we can write:
\[ x < 5.5 \]
This is the final inequality.